Abstract

On the basis of an analysis of the autocovariance of the complex heterodyne signal, some novel algorithms are derived and investigated for recovering the nonuniform Doppler-velocity coherent-lidar profiles within the lidar resolution interval conditioned by the sensing laser-pulse length. The case of exponentially shaped sensing laser pulses is considered. The algorithm performance and efficiency are studied and illustrated by computer simulations (based on the use of pulse models and real laser pulses), taking into account the influence of additive noise and radial-velocity fluctuations. It is shown that, at some reasonable number of signal realizations used and with appropriate data processing to suppress the noise effects, the Doppler-velocity profiles can be determined with a considerably shorter resolution interval in comparison with that (usually accepted as a lower bound) determined by the pulse length.

© 2002 Optical Society of America

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  1. M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
    [Crossref] [PubMed]
  2. R. Frehlich, S. M. Hannon, S. W. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
    [Crossref] [PubMed]
  3. S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
    [Crossref]
  4. L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “High-resolution Doppler-velocity estimation techniques for processing of coherent heterodyne pulsed lidar data,” J. Opt. Soc. Am. A 18, 134–142 (2001).
    [Crossref]
  5. T. J. Kane, J. D. Kmetec, “Diode pumped Tm:YAG laser radar transceiver,” in Coherent Laser Radar, Vol. 19 of the 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 285–288.
  6. S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
    [Crossref]
  7. J. Liu, D. Shen, S.-C. Tam, Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron. 37, 888–896 (2001).
    [Crossref]
  8. J. Dong, P. Deng, Y. Liu, Y. Zhang, J. Xu, W. Chen, X. Xie, “Passively Q-switched Yb:YAG laser with Cr4+:YAG as the saturable absorber,” Appl. Opt. 40, 4303–4307 (2001).
    [Crossref]
  9. T. Kondoh, S. Lee, D. P. Hutchinson, R. K. Richards, “Collective Thomson scattering using a pulsed CO2 laser in JT-60U,” Rev. Sci. Instrum. 72, 1143–1146 (2001).
    [Crossref]
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    [Crossref] [PubMed]
  11. A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 1: Single Scattering and Transport Theory (Academic, New York, 1978).
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  13. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Appl. Opt. 5, 1588–1594 (1966).
    [Crossref] [PubMed]
  14. L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Deconvolution techniques for improving the resolution of long-pulse lidars,” J. Opt. Soc. Am. A 10, 2296–2306 (1993).
    [Crossref]
  15. L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Pulse backscattering tomography based on lidar principle,” Opt. Commun. 151, 339–352 (1998).
    [Crossref]
  16. J. H. Churnside, H. T. Yura, “Speckle statistics of atmospherically backscattered laser light,” Appl. Opt. 22, 2559–2565 (1983).
    [Crossref] [PubMed]
  17. G. M. Ancellet, R. T. Menzies, “Atmospheric correlation-time measurements and effects on coherent Doppler lidar,” J. Opt. Soc. Am. A 4, 367–373 (1987).
    [Crossref]
  18. Ph. Salamitou, A. Dabas, P. Flamant, “Simulations in the time domain for heterodyne coherent laser radar,” Appl. Opt. 34, 499–506 (1995).
    [Crossref] [PubMed]
  19. I. N. Bronstein, K. A. Semendjajew, Taschenbuch der Mathematik (Nauka, Moscow, and Teubner, Leipzig, 1989).
  20. V. I. Tatarski, Wave Propagation in Turbulent Atmosphere (Nauka, Moscow, 1967).
  21. R. W. Hamming, Digital Filters (Prentice-Hall, Englewood Cliffs, N.J., 1983).
  22. K. S. Miller, M. M. Rochwarger, “A covariance approach to spectral moment estimation,” IEEE Trans. Inform. Theory IT-18, 588–596 (1972).
    [Crossref]

2001 (4)

J. Liu, D. Shen, S.-C. Tam, Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron. 37, 888–896 (2001).
[Crossref]

T. Kondoh, S. Lee, D. P. Hutchinson, R. K. Richards, “Collective Thomson scattering using a pulsed CO2 laser in JT-60U,” Rev. Sci. Instrum. 72, 1143–1146 (2001).
[Crossref]

L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “High-resolution Doppler-velocity estimation techniques for processing of coherent heterodyne pulsed lidar data,” J. Opt. Soc. Am. A 18, 134–142 (2001).
[Crossref]

J. Dong, P. Deng, Y. Liu, Y. Zhang, J. Xu, W. Chen, X. Xie, “Passively Q-switched Yb:YAG laser with Cr4+:YAG as the saturable absorber,” Appl. Opt. 40, 4303–4307 (2001).
[Crossref]

1998 (1)

L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Pulse backscattering tomography based on lidar principle,” Opt. Commun. 151, 339–352 (1998).
[Crossref]

1997 (1)

1995 (1)

1994 (1)

S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
[Crossref]

1993 (1)

1990 (2)

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
[Crossref] [PubMed]

1987 (1)

1983 (1)

1982 (1)

1972 (1)

K. S. Miller, M. M. Rochwarger, “A covariance approach to spectral moment estimation,” IEEE Trans. Inform. Theory IT-18, 588–596 (1972).
[Crossref]

1966 (1)

Ancellet, G. M.

Breguet, J.

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

Bronstein, I. N.

I. N. Bronstein, K. A. Semendjajew, Taschenbuch der Mathematik (Nauka, Moscow, and Teubner, Leipzig, 1989).

Chen, W.

Churnside, J. H.

Cupp, R. E.

Dabas, A.

Deng, P.

Dong, J.

Dreischuh, T. N.

Flamant, P.

Frehlich, R.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Gurdev, L. L.

Hamming, R. W.

R. W. Hamming, Digital Filters (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Hannon, S. M.

R. Frehlich, S. M. Hannon, S. W. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
[Crossref] [PubMed]

S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
[Crossref]

Henderson, S. W.

Hutchinson, D. P.

T. Kondoh, S. Lee, D. P. Hutchinson, R. K. Richards, “Collective Thomson scattering using a pulsed CO2 laser in JT-60U,” Rev. Sci. Instrum. 72, 1143–1146 (2001).
[Crossref]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 1: Single Scattering and Transport Theory (Academic, New York, 1978).

Kane, T. J.

T. J. Kane, J. D. Kmetec, “Diode pumped Tm:YAG laser radar transceiver,” in Coherent Laser Radar, Vol. 19 of the 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 285–288.

Kmetec, J. D.

T. J. Kane, J. D. Kmetec, “Diode pumped Tm:YAG laser radar transceiver,” in Coherent Laser Radar, Vol. 19 of the 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 285–288.

Kondoh, T.

T. Kondoh, S. Lee, D. P. Hutchinson, R. K. Richards, “Collective Thomson scattering using a pulsed CO2 laser in JT-60U,” Rev. Sci. Instrum. 72, 1143–1146 (2001).
[Crossref]

Lam, Y.-L.

J. Liu, D. Shen, S.-C. Tam, Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron. 37, 888–896 (2001).
[Crossref]

Lee, S.

T. Kondoh, S. Lee, D. P. Hutchinson, R. K. Richards, “Collective Thomson scattering using a pulsed CO2 laser in JT-60U,” Rev. Sci. Instrum. 72, 1143–1146 (2001).
[Crossref]

Liu, J.

J. Liu, D. Shen, S.-C. Tam, Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron. 37, 888–896 (2001).
[Crossref]

Liu, Y.

Luethy, W.

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

Menzies, R. T.

Miller, K. S.

K. S. Miller, M. M. Rochwarger, “A covariance approach to spectral moment estimation,” IEEE Trans. Inform. Theory IT-18, 588–596 (1972).
[Crossref]

Ostroumov, V.

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

Post, M. J.

Richards, R. K.

T. Kondoh, S. Lee, D. P. Hutchinson, R. K. Richards, “Collective Thomson scattering using a pulsed CO2 laser in JT-60U,” Rev. Sci. Instrum. 72, 1143–1146 (2001).
[Crossref]

Rochwarger, M. M.

K. S. Miller, M. M. Rochwarger, “A covariance approach to spectral moment estimation,” IEEE Trans. Inform. Theory IT-18, 588–596 (1972).
[Crossref]

Salamitou, Ph.

Schnell, S.

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

Semendjajew, K. A.

I. N. Bronstein, K. A. Semendjajew, Taschenbuch der Mathematik (Nauka, Moscow, and Teubner, Leipzig, 1989).

Shcherbakov, I.

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

Shen, D.

J. Liu, D. Shen, S.-C. Tam, Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron. 37, 888–896 (2001).
[Crossref]

Siegman, A. E.

Stoyanov, D. V.

Tam, S.-C.

J. Liu, D. Shen, S.-C. Tam, Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron. 37, 888–896 (2001).
[Crossref]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in Turbulent Atmosphere (Nauka, Moscow, 1967).

Thomson, J. A.

S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
[Crossref]

Wang, J. Y.

Weber, H.

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

Xie, X.

Xu, J.

Yura, H. T.

Zhang, Y.

Appl. Opt. (7)

IEEE J. Quantum Electron. (2)

S. Schnell, V. Ostroumov, J. Breguet, W. Luethy, H. Weber, I. Shcherbakov, “Acoustooptic Q switching of erbium lasers,” IEEE J. Quantum Electron. 26, 1111–1114 (1990).
[Crossref]

J. Liu, D. Shen, S.-C. Tam, Y.-L. Lam, “Modeling pulse shape of Q-switched lasers,” IEEE J. Quantum Electron. 37, 888–896 (2001).
[Crossref]

IEEE Trans. Inform. Theory (1)

K. S. Miller, M. M. Rochwarger, “A covariance approach to spectral moment estimation,” IEEE Trans. Inform. Theory IT-18, 588–596 (1972).
[Crossref]

J. Mod. Opt. (1)

S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
[Crossref]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

L. L. Gurdev, T. N. Dreischuh, D. V. Stoyanov, “Pulse backscattering tomography based on lidar principle,” Opt. Commun. 151, 339–352 (1998).
[Crossref]

Rev. Sci. Instrum. (1)

T. Kondoh, S. Lee, D. P. Hutchinson, R. K. Richards, “Collective Thomson scattering using a pulsed CO2 laser in JT-60U,” Rev. Sci. Instrum. 72, 1143–1146 (2001).
[Crossref]

Other (6)

T. J. Kane, J. D. Kmetec, “Diode pumped Tm:YAG laser radar transceiver,” in Coherent Laser Radar, Vol. 19 of the 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 285–288.

A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 1: Single Scattering and Transport Theory (Academic, New York, 1978).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

I. N. Bronstein, K. A. Semendjajew, Taschenbuch der Mathematik (Nauka, Moscow, and Teubner, Leipzig, 1989).

V. I. Tatarski, Wave Propagation in Turbulent Atmosphere (Nauka, Moscow, 1967).

R. W. Hamming, Digital Filters (Prentice-Hall, Englewood Cliffs, N.J., 1983).

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Figures (8)

Fig. 1
Fig. 1

Model of the wind-vortex-like distribution of the radial velocity along the line of sight.

Fig. 2
Fig. 2

Models of the profile Φ(z) and (inset) the exponentially shaped laser pulse.

Fig. 3
Fig. 3

Real laser-pulse shapes (dashed-dotted and solid curves) and corresponding exponentially shaped approximations (dotted and dashed curves) used in the simulations.

Fig. 4
Fig. 4

Doppler-velocity profiles v r (z) restored by use of (a) algorithm (13) and (b) algorithm (14). The original profile v(z) (dashed curve) and the profile resulting from applying a pulse-pair algorithm (dotted curve) are given for comparison.

Fig. 5
Fig. 5

Doppler-velocity profiles v r (z) (dotted curves) restored by use of (a) algorithm (13) and (b) algorithm (14) in the presence of uncorrelated additive noise. The original profile v(z) (dashed curve) and the profiles restored in the absence of additive noise (solid curves) are given for comparison. The actual SNR, SNR a (z), is indicated by the dashed-dotted curve.

Fig. 6
Fig. 6

Doppler velocity profiles v r (z) restored by use of algorithm (13) in the presence of correlated additive noise with (solid curve) and without (dotted curve) compensation of the bias of the autocovariance estimate. The original profile v(z) (dashed curve) is also shown.

Fig. 7
Fig. 7

Doppler-velocity profiles v r (z) recovered on the basis of (a) algorithm (13) and (b) algorithm (14) in the presence of uncorrelated velocity fluctuations with σ = 4 m/s (dotted curves) and turbulent (correlated) velocity fluctuations with σ = 2 m/s (solid curves). The original profile v(z) (dashed curve) is given for comparison.

Fig. 8
Fig. 8

Original Doppler-velocity profile (solid curve) and two profiles, restored by algorithm (14), resulting from simulations in which real laser pulses were used for synthesis of the coherent-lidar signal. The dashed and the dotted curves correspond to the dashed-dotted and the solid shapes in Fig. 3.

Equations (21)

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E0r, t=PArf0t-z/cexpjω0t-z/c+0t-z/cδωcht+δωrtdt+φort-z/c+φ0,
It=Jt+jQt=K  Ebρt, t · Eh*ρt, tdρt,
It=2z/c=expjφ0-φht×l=l1+1l2 f0t-2zl/cdAzlexpjωmzlt+jφωdt-2zl/cχzl+jφort-2zl/cχzl,
Pt=2z/c=z0ct/2 ft-2z/cΦzdz,
Pt=2z/c=Pmrt=2z/c=cτeff/2Φct/2,
dAzl=K nexp-2jkDlz0lnAρln, zlanl·  Ah*ρtGρt; ρln, zldρt,
Covt, θ=z0ct/2dzf0t-2z/cf0t+θ-2z/cΦzexpjωmzθ+Δφcht, θ, zζt, θ, zξt, θ, z×γz, 2ω0θ/c,
Δφcht, θ, z=φcht+θ-2z/cχz-φcht-2z/cχz,
ζt, θ, z=expjφωrt+θ-2z/cχz-jφωrt-2z/cχz,
ξt, θ, z=expjφort+θ-2z/cχz-jφort-2z/cχz,
Δφcht, θ, z=φchIt-2z/cχzθχz=δωcht-2z/cχzθχz,
ζt, θ, z=expjφωrIt-2z/cχzθχz=exp{jδωrt-2z/cχzθχz,
ξt, θ, z=expjφorIt-2z/cχzθχz.
ζθχz= pδωrexpjδωrθχzdδωr,
ξθχz= pφorIexpjφorIθχzdφorI.
f0ϑf0ϑ+θ=fmϑfmϑ+θηϑ, θ,
Covt, θ=z0ct/2dzfmt-2z/cfmt+θ-2z/cηθΦzexpjωmzθ+δωcht-2z/cχzθχz×ζθχzξθχzγz, 2ω0θ/c.
Γt, θ=CovtttIIIt, θ+6/τCovttIIt, θ+12/τ2CovtIt, θ+8/τ3Covt, θ =ce/τ2 exp-θ/τζθξθηθψt, θ×expjωmz=ct/2θ1+θ/τ+θψt, θtI/2ψt, θ+jωmz=ct/2tIθ2/2,
ωmz=ct/2=θ-1arctanIm Γt, θ/Re Γt, θ.
ωmz=ct/2=Im Gt/Φz=ct/2ce2η0/τ2,
Covˆt, θ=mΔt=N-1k=1NIkt+nkt*Ikt+mΔt+nkt+mΔt,

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